San Francisco 49ers fans celebrate during the fourth quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: John Storey, Special To The Chronicle

San Francisco 49ers fans celebrate during the fourth quarter of the...

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49ers coach Jim Harbaugh during the first half of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: John Storey, Special To The Chronicle

49ers coach Jim Harbaugh during the first half of the San Francisco...

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Offensive tackle Joe Staley (74) blocks for Running back LaMichael James (23) during the first half of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: John Storey, Special To The Chronicle

Offensive tackle Joe Staley (74) blocks for Running back LaMichael...

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49ers Running back LaMichael James (23) is brought down by Arizona Cardinals safety Kerry Rhodes (25) and defensive end Calais Campbell (93) during the first half of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: John Storey, Special To The Chronicle

49ers Running back LaMichael James (23) is brought down by Arizona...

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Kicker David Akers (2) after he misses his second field goal attempt during the second quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: John Storey, Special To The Chronicle

Kicker David Akers (2) after he misses his second field goal...

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Wide receiver Michael Crabtree (15) celebrates after a long catch downfield int he second quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

Wide receiver Michael Crabtree (15) celebrates after a long catch...

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Wide receiver Michael Crabtree (15) catches a touchdown pass from Quarterback Colin Kaepernick (7) during the second quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

Wide receiver Michael Crabtree (15) catches a touchdown pass from...

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Running back Anthony Dixon (24) during the third quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

Running back Anthony Dixon (24) during the third quarter of the San...

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Wide receiver Michael Crabtree (15) celebrates by throwing the ball into the stands after a touchdown in the third quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

49ers Wide receiver Michael Crabtree (15) celebrates with Wide receiver Ted Ginn Jr. (19) following his third touchdown of the game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

49ers Wide receiver Michael Crabtree (15) celebrates with Wide...

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Running back Frank Gore (21) runs through tackle by Arizona Cardinals safety Adrian Wilson (24) during the second half of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: John Storey, Special To The Chronicle

Running back Frank Gore (21) runs through tackle by Arizona...

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San Francisco 49ers Wide receiver Michael Crabtree (15) during the second half of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: John Storey, Special To The Chronicle

San Francisco 49ers Wide receiver Michael Crabtree (15) during the...

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San Francisco 49ers Quarterback Colin Kaepernick (7) during the second half of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

A cheerleader with the San Francisco 49ers Gold Rush dances during a NFL football game between the San Francisco 49ers and Arizona Cardinals at Candlestick Park in San Francisco, Calif. on Sunday, December 30, 2012.

Photo: Stephen Lam, Special To The Chronicle

A cheerleader with the San Francisco 49ers Gold Rush dances during...

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San Francisco 49ers wide receiver Michael Crabtree (15) is surrounded by members of the media after the team's 27-13 victory over the visiting Arizona Cardinals at Candlestick Park in San Francisco, Calif. on Sunday, December 30, 2012.

Photo: Stephen Lam, Special To The Chronicle

San Francisco 49ers wide receiver Michael Crabtree (15) is...

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San Francisco 49ers quarterback Alex Smith (11) waves to the fans as he leaves the field after the team's 27-13 victory over the visiting Arizona Cardinals at Candlestick Park in San Francisco, Calif. on Sunday, December 30, 2012.

Photo: Stephen Lam, Special To The Chronicle

San Francisco 49ers quarterback Alex Smith (11) waves to the fans...

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Frank Gore, who rushed for 68 yards on 20 carries, gives a hug to 49ers co-owner Denise DeBartolo York in the waning moments of Sunday's victory.

Photo: Carlos Avila Gonzalez, The Chronicle

Frank Gore, who rushed for 68 yards on 20 carries, gives a hug to...

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San Francisco 49ers Running back Frank Gore (21) celebrates after scoring a touchdown in the fourth quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

San Francisco 49ers Running back Frank Gore (21) celebrates after...

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Colin Kaepernick comes off the field after the game ended. The San Francisco 49ers played the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday, December 30, 2012, in the final game of the 2012 season.

Photo: Carlos Avila Gonzalez, The Chronicle

Colin Kaepernick comes off the field after the game ended. The San...

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Colin Kaepernick, who passed for 276 yards and two touchdowns, runs toward the left sideline in the fourth quarter.

Photo: Carlos Avila Gonzalez, The Chronicle

Colin Kaepernick, who passed for 276 yards and two touchdowns, runs...

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San Francisco 49ers dressed like Wide receiver Michael Crabtree fans celebrate the Niners win in the stands following the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Stephen Lam, Special To The Chronicle

San Francisco 49ers dressed like Wide receiver Michael Crabtree...

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San Francisco 49ers Defensive tackle Isaac Sopoaga (90) throws his show into the stands following the San Francisco 49ers win over the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

San Francisco 49ers Defensive tackle Isaac Sopoaga (90) throws his...

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San Francisco 49ers kicker David Akers (2) is being consoled by tight end Garrett Celek (81) after missing a second field goal missing a field goal during the first half of his NFL football game against Arizona Cardinals at Candlestick Park in San Francisco, Calif. on Sunday, December 30, 2012.

Photo: Stephen Lam, Special To The Chronicle

San Francisco 49ers kicker David Akers (2) is being consoled by...

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the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

the San Francisco 49ers game against the Arizona Cardinals at...

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Alex Smith hands the ball off to LaMichael James in the fourth quarter. Smith came in to the game for the final two 49ers drives. The San Francisco 49ers played the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday, December 30, 2012, in the final game of the 2012 season.

Photo: Carlos Avila Gonzalez, The Chronicle

Alex Smith hands the ball off to LaMichael James in the fourth...

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Candlestick Park is seen reflected from a puddle of water as fans gather to tailgate prior the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Stephen Lam, Special To The Chronicle

Candlestick Park is seen reflected from a puddle of water as fans...

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Ahmed Almalik, of San Francisco, displays pieces of 49ers jewelries in the parking lot outside Candlestick Park prior to a NFL football game between the San Francisco 49ers and Arizona Cardinals in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Stephen Lam, Special To The Chronicle

Ahmed Almalik, of San Francisco, displays pieces of 49ers jewelries...

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Fans head to their seats before the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

Fans head to their seats before the San Francisco 49ers game...

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San Francisco 49ers Running back Frank Gore (21) scores a touchdown during the fourth quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Quarterback Colin Kaepernick (7) celebrates with Wide receiver Michael Crabtree (15) and Offensive tackle Joe Staley (74) after a Crabtree touchdown in the third quarter of the San Francisco 49ers game against the Arizona Cardinals at Candlestick Park in San Francisco, Calif., on Sunday December 30, 2012.

Photo: Carlos Avila Gonzalez, The Chronicle

Quarterback Colin Kaepernick (7) celebrates with Wide receiver...

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The San Francsico 49ers vs. the Arizona Cardinals at Candlestick Park in San Francisco on Sunday, November 30th, 2012.

After they didn't show up for the first quarter Sunday, things brightened considerably for the 49ers.

Now they don't have to show up for the first round of the playoffs.

San Francisco shook off a sluggish start and dismissed the hapless Cardinals 27-13 in its regular-season finale to claim its second straight NFC West division title. Then, roughly 30 minutes after the victory, the television-watching 49ers celebrated again in the locker room when the Vikings beat the Packers 37-34 on a last-second field goal.

With Minnesota's win, the 49ers earned the No. 2 seed and a first-round bye. They will host a divisional playoff game at 5 p.m. Jan. 12 at Candlestick Park.

How big a deal is a bye after eight straight weeks of NFL games?

"I need it," center Jonathan Goodwin said. "I think I have about 20 bruises on my body right now. And I'm not exaggerating."

The locker-room roar that erupted when Minnesota's Blair Walsh drilled a 29-yard field goal late Sunday afternoon contrasted sharply with the silence at Candlestick during a desultory opening by the home team.

After 16 minutes, Arizona (5-11) led 6-0 and had outgained the 49ers 134 yards to 15.

Considering the Cardinals' 32nd-ranked offense entered with a who's-that cast featuring quarterback Brian Hoyer and running back William Powell, each making his first career start, it appeared the 49ers would remain forever toothless with All-Pro tackle Justin Smith sidelined by a partially torn triceps.

After that fall into an early hole, though, defensive tackle Ray McDonald said he and his teammates were awakened by a realization: They actually could lose to a team that entered with 10 losses in its past 11 games.

"We were like 'Man, we've got to win this game,' " McDonald said. "It's going to be on our backs. The offense is depending on us to get some stops."

The defense did its part: After its promising start, Arizona managed 128 yards and five first downs in the game's final 44 minutes. The Cardinals didn't score again until a 37-yard touchdown pass from Hoyer to Michael Floyd with 1:59 left.

Meanwhile, the 49ers' offense, which went three-and-out on its first three possessions and drew a derisive cheer when it managed its initial first down in the second quarter, found its rhythm.

With only two wide receivers with more than two catches this season, it appeared quarterback Colin Kaepernick might struggle from a lack of pass-catching options. He eventually discovered a solution: Fling it to Michael Crabtree.

The fourth-year wide receiver had eight catches for a career-high 172 yards and two touchdowns. His yardage total was the most by a San Francisco receiver since Terrell Owens had 191 on Nov. 3, 2002. Crabtree (1,105 yards) also became the 49ers' first receiver to post a 1,000-yard season since Owens did so in 2003.

Crabtree had 548 receiving yards - roughly half of his season total - in Kaepernick's final five starts.

"My dude made it happen," Crabtree said, referring to the second-year quarterback. "I'm just going out there, running routes, catching the ball until I make a play."

Arizona head coach Ken Whisenhunt had seen enough of Crabtree running Pro Bowl cornerback Patrick Peterson ragged. In two games against the Cardinals, Crabtree had 13 catches, 244 yards and four touchdowns.

"He's a good player, at least in the games that he's played against us," Whisenhunt said. "But Patrick hasn't played very well against him, either. It seems like we can't tackle that guy."

Thanks, in part, to Crabtree's performance, the 49ers' ugly opening was largely forgotten in a celebratory locker room. When the game began, it appeared the 49ers would stumble into the postseason, but three hours later, they were assured of entering the playoffs rested.

For that, tight end Delanie Walker offered a heartfelt message to the Vikings: